I am interesting in writing a complete code for the Hartree-Fock method to improve my understanding of it. It seems relatively complex in three dimensions, so I am wondering if it would be simpler in two dimensions and also how to start. I have read a decent bit of theory, but my understanding is still not great. Any practical pointers would be very much appreciated!

I'm thinking of using the 2D equivalent of hydrogenoid orbitales as basis function (ergo a circle, an "8" shape, ...). This should simplify the calculation of the integrals.

I think that I do not truly understand how to numerically solve the Schrödinger equation to obtain a first energy value. Hopefully there exists some resource to clarify this!